You’re on the right track. I would add the column “Constraint Type” to my view (Right click on the column titles, Insert Column, select “Constraint Type”. Then you can make the first one “As Soon As Possible” and copy it down to all of the rest of the tasks. This will wipe out your Constraint Date.
I’m assuming you tried selecting all and then just changing it to “As Soon As Possible” in the Task Details Form window. That will not work to change all the tasks.